A Lattice Point Problem and Additive Number Theory

  title={A Lattice Point Problem and Additive Number Theory},
  author={Noga Alon and Moshe Dubiner},
For every dimension d ≥ 1 there exists a constant c = c(d) such that for all n ≥ 1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues. 

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Ein Extremalproblem für Gitterpunkte

  • H. Harborth
  • J. Reine Angew. Math. 262/263
  • 1973
Highly Influential
4 Excerpts

An application of graph theory to additive number theory

  • I. Z. Ruzsa
  • Scientia 3
  • 1989
2 Excerpts

A problem on lattice points

  • B. Leeb, C. Stahlke
  • Crux Mathematicorum 13
  • 1987
1 Excerpt

Rödl , On subsets of abelian groups with no 3term arithmetic progression

  • R. L. Graham P. Frankl, V.
  • J . Combinatorial Theory Ser . A
  • 1987

An ergodic Szemerédi theorem for IP-systems and combinatorial theory

  • H. Furstenberg, Y. Katznelson
  • J. d’Analyse Math. 45
  • 1985
1 Excerpt

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